PL-OM 1988 Problem 1

The real numbers $x_1, x_2, ... , x_n$ belong to the interval $(0,1)$ and satisfy $x_1 + x_2 + ... + x_n = m + r$ , where $m$ is an integer and $r \in [0,1)$ . Show that $x_1 ^2 + x_2 ^2 + ... + x_n ^2 \leq m + r^2$ .